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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A normal distribution is a common assumption underlying many statistical tests. Although the assumption is usually not important, it is possible to test whether it is plausible. Specifically, the unit normal table lists proportions for individual sections of a normal distribution, and a chi-square test for goodness of fit can be used to evaluate whether a specific distribution fits the proportions. For example, if a normal distribution is divided into sections using z-score values, then proportions in each section should be as follows:

  -1.5 < z -0.5 <z 0.5 <z  
z < -1.5 -0.5 0.5 1.5 z > 1.5
6.68% 24.17% 38.30% 24.17% 6.68%

Use these proportions to test whether the following sample of n = 90 scores is significantly different from a normal distribution. Test with a = .05.

  -1.5 < z -0.5 <z 0.5 <z  
z < -1.5 -0.5 0.5 1.5 z > 1.5
8 19 31 23 9

To determine

To Test: If there is significant difference between the observed values and normal distribution.

Explanation

Given info:

Observed values:

Z<1.5 1.5<Z<1.5 1.5<Z<1.5 1.5<Z<1.5 Z>1.5
8 9 31 23 9

Expected values:

Z<1.5 1.5<Z<0.5 0.5<Z<0.5 0.5<Z<1.5 Z>1.5
6.68% 24.17% 38.30% 24.17% 6.68%

n=90α=5%

Calculation:

The expected values can be rewritten as frequency as follows:

fe=fe%×90

Thus, the expected values are as follows:

6.012, 21.753, 34.47, 21.753, 6.012

χ2=(fofe)fe

The following table summarizes the calculations:

Cell fo fe</

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